statistics in the nz curriculum stocktake

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NZ Statistical Association Education Committee: For NZ Curriculum Stocktake Group; 21 Oct 03

Statistics in the NZ Curriculum Stocktake

Mike Camden

NZ Statistical Association Education CommitteeMike: [email protected]

NZSA: http://www.stat.auckland.ac.nz/nzsa/

NZSA Newsletter: http://nzsa.rsnz.govt. nz/newsletter58

Health warning: The views in here belong- Either to the Stat Assoc Education Committee- Or to Mike - Or to both.They are not intended as the views of Statistics New Zealand.

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Proposed Contents of Session: A Club Sandwich

Stats in Schools: Intros, multchoice test and the big ideas

Workshop 1: Skills for a “Hot Off The Press”

Background, illustrations, opinions and more illustrations

Workshop 2: Stats and your Essential Learning Area

Conclusion: The chocolate investigation; What Now.

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Deterministic and Stochastic ThoughtGreek: Stokhastikos: Person who aims, targets, forecasts

Stokhos: An aim, target

English: Stochastic: involving ‘random’ probability distributions

There’s an ELA called…

MathsMaths and StatsMaths and Stats and Probability

There’s a bunch of mental tools (“Maths”) with two sides:

Deterministic thinking and modellingStochastic thinking and modelling

They’ve both been around since humans stood up, started talking and drawing, and invented Education!

See Paper 8 in http://wwwmaths.anu.edu.au/other/ncms/mathsdocs/Mumford, D (1999). The dawning of the age of Stochasticity.

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Some odd things about Stats:“Maths” has two sides:

Deterministic and Stochastic

Stats (and Probability) is entangled with….Language: English, Te Reo Maori, the othersGraphics and visual communicationContext: all the ELAsMaths

Stats supports active learning in other ELAsvia “investigations”

“Entangled” has two directions …….

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The big questions for this session:Three questions:1: How do we build Curriculum so that Stats supports your

ELA?2: How do we build Curriculum so that your ELA supports

Stats?3: How can Curriculum trigger students into enjoying and

valuing both your ELA and Stats?

JFK’s version (with stochastic input):And so, my fellow educators, ask not what your ELA can do for Stats; ask what Stats can do for your ELA.

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A Multichoice Test: Q 1 of 3: for Achievement:The NZ Stat Assoc Education Committee’s aim is:

A: Stuff Stats into every crack in the Curriculum

B: Chuck half the Maths and replace it with Stats

C: Streamline the Stats and Insert the Interconnectivity among ELAs

(Yes, I did read the Listener!!)

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A Multichoice Test: Q 2 of 3: for Merit:The Essence of Stats is:

A: Weird graphs with kinky names

B: Weird stuff like 2 = (x – )2/ n

C: Investigations, contexts, datasets, variability, exploration, conclusions, communication

Which one would look good in the Maths and Stats Essence Statement??

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A Multichoice Test: Q 3 of 3: for Excellence:Life and the tools we make for enjoying it are

A: Mostly deterministic

B: Mostly stochastic

C: Basically stochastic, but deterministic models are often good working approximations.

Hint: Best answer in each Question is C.

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Stats in Schools: The big ideas: 1/3Stats is quite different from the rest of Maths (our old theme)

and so needs very careful treatmentStats and the rest of Maths stand together (our new theme)

giving stochastic and deterministic models of lifeStochastic (ie, variable) aspects of life are becoming more

obvious: technology, environment, social policy …Some front-end statistical methods are …

fun, commonsense, graphical and suddenly accessible to school students

Context is hugely important in statistical thinking which is where you come in!

Stats in the Curriculum must meet the needs of the parties to the Treaty of Waitangi

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Stats in Schools: The big ideas: 2/3Stats needs careful curriculum links with …

the other Maths strandsthe other essential learning areasthe other layers in the Framework: Principles, Future Focused Themes, Skills, Values, AttitudesIs there a literature on this??

We need a new engine for Stats curriculum, assessment, professional development, resource making

We need a plan to build capability in Stats Pedagogy in NZ

The NZ Stats Community is aware, alert, offering its insights They want NZ to get the Stats right!

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Stats in Schools: The big ideas: 3/3Graphical data exploration (data visualisation) is profound,

powerful, accessible but takes lots of learning (ie, practice with datasets; yours!!).It must not be seen as trivial!

Any Learning Area can link with Stats so that … both are valued as enjoyable and useful

We’re at the forefront …Dammit!!!

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A Scalpel for Stats Curriculum ConstructorsAny investigation has these stages:State the purpose, get approvalDesign and/or plan all aspects of itCollect the data into a Unit Record DatasetEdit/Launder/Clean the dataset with graphs etcExplore and/or analyse the dataset with graphs etc

John Tukey: “If you haven’t done a graph, then you haven’t done an analysis”

Summarise the findings/information/conclusionsCommunicate the Conclusions

with words, numbers and graphs working together(Edwin Tufte: The visual display of quantitative information)

Lets give up writing “Present the Data with Graphs” forever.

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Another Scalpel:Any dataset that is remotely useful or interesting has several related variables:We stop pretending that variables ever occur alone.We replace ‘bi-variate data’and ‘multi-variate data’ by‘dataset’.

This thing’s a DatasetThis thing’s a (Frequency) Table

Name Favourite Fruit

Gender

Trevor Mango Boy

Steve Apple Boy

Marion Apple Girl

Turiana Apple Girl

Count

Gender Girl Boy

Fruit

Apple 2 1

Mango 0 1

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Workshop 1: Skills: what, where, howSee SNZ’s “Hot Off The Press”,

NZ Income Survey June 2003 Quarter; 1 Oct 03.

Assume we want all NZers to be able to read, use and critique things like this.

1 What skills, attitudes and values do they need?

2 Whereabouts do we put these skills etc in the Curriculum Framework??

3 What does NZ need, to ensure effective teaching, learning and assessment of the skills etc???

4 Are we in the right Industry????(See Table 10 near the end)

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The Middle Bit:Background, illustrations, opinions, more illustrations …

Mussels (Mytius Edulis): Chaffers Marina:

Shell Vol(ml) vs Shell Length (mm)Stochastic and deterministic views

051015202530354045

0 20 40 60 80 100

ShellVol

Cubic

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Some of the Communities of Interest in Maths EdNZSA, its Education Com, Maths Teachers and Curric Makers

The intersections are very small.

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NZ Statistical Association Education Committee’s conclusionsOn Thur 11 Sept 03, the Committee discussed the Stocktake

at length. Main conclusion: it offers to:Make input into and review the draft Framework documentBe part of research projects that would underpin

curriculum and resource writingTake a leadership role in the writing of the Statistics strand

of the Curriculum document

On Thur 9 Oct, it met with MoE people and discussed:Making input into Stats in the whole curriculum

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Health Report for the Statistics Strand in MathsBone structure mostly good but needs a hip replacement and some physio elsewhereSoft tissue functioning but needs several cut-and-tuck operations, several shots of Botox and a body-building programme at the gym; weight-watchers programme not indicated. Badly needs a hair transplant.Socialisation: (the main problem for us today) needs a ”how to win friends and influence people” course.

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Biology Part 1: Stats in NCEA Biology Level 3Explanatory Note 7: Recording and processing

Data processing would usually involve calcs and graphing (Good!) to establish a relevant pattern or trend. Stat. procedures, where approp., should be used to establish the reliability (??) of the data e.g. mean, standard deviation, confidence intervals, standard error, difference between two means, ANOVA (??), Chi squared test(??).

Sufficient data involves repeats, trials, appropriate range for the independent variable (Exp Design??), appropriate samp size.

Systematically record means data will be presented in a way (eg table, tally chart) that allows it to be interpreted without reference to the method. (??)

See NZSA Newsletter Sept 03: Gwenda Hill; Stats more advanced (more mathematical?) in Biology than in Maths for NCEA L3

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Biology Part 2: Views of senior NZ biometriciansIan Westbrooke; Dept of Conservation; NZSA Conf Jul 03:

Staff’s (university) stats education has been on hypothesis tests and ANOVAs.

What they need isconfidence intervals that can lead to management decisions, and Exploratory Data Analysis (with graphs)

Harold Henderson, Agresearch; NZAMT8; Jul 03:(Bevan Werry speech)

Powerful new methods of data visualisation… produce a new frontier of data analysis. Visualisation tools provide deep insight into the structure of data…. Dynamic statistical graphics are now widely available….

Using these, the internal components of NCEA (L3) statistics can be presented by students in ways that are relevant, up-to-date and easy to understand.

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Biology Part 3: the morals:What we can and should do in Stats is changing profoundly

and fast

How do we assure Statistics (and Maths) their most useful places in all the learning areas?

How can we make the NZ Curriculum Engine produce 21st century objectives??

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The fun of the fair: Reflections on the Wellington Science Fair:Impressive statistics from 8 of the 400 Year 7 and 8 peopleThe essence of statistical quality for statistics judges

designreplicationgraphs that show variabilityconclusions

Science, years 7 and 8, seems to do much of the Experimental Design that has been removed from our NCEA L3!

But we don’t provide the commonsense graphic tools needed.Reflections on the Canterbury and W Coast Science FairWinners had their raw data well displayed,

and were able to deal with its variability.

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The Point of Inflection in Maths Education HistoryStatistics is very different from the rest of Maths in…Its rate of change and its age

(it is embryonic or possibly adolescent)The contexts and ways in which it gets used

(and therefore the ways it can be valued)The way in which today’s complex world of technology

and social needs depends on itThe ways it can be taught, learned and assessed

(the pedagogy…. And the pedagogues!!)The ways in which it uses computer technologyThe ways it can be integrated with other learning areasTeacher confidence, professional development needs and

resource needs, in Maths and other ELAs

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Rabid Opinions 1 of 2Values

Stats is founded on a Value:information-based decision-making.

Curriculum and Assessment for Stats:We must make sure the engine pulls the carriage, and not the other way round.

A fourth stage in Statistical education??Stage 1: Traditional (what we got, and forgot!)Stage 2: Reformed (Data and EDA-based)Stage 3: Transformed (Value-based)Stage 4: Blossoming!! (Real issues, great data, dynamic software. It really is new.)

Stats and Maths thinking are different; stats can’t be taught as is it were maths

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Rabid Opinions 2 of 2Hardware and Software: We’ve got to have it:

In biology, chemistry, physics, geography, cooking, clothing, PE, …, students use the real tools and materials of the subject.So must Stats!The tools are the computer hardware and software;The materials are the datasets from the other ELAs.

Students enjoy hands-on work with data, owning projects and completing investigations

The Forefront in Stats education:NZ was there, but is now lagging behind.We need to address this, with your help

The Essential Skill Numeracy needs to stay, andto be enhanced with Stat Reasoning, Thinking and Literacy.

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Tupaia and JamesOct 1769; the Endeavour sails from Tahiti to NZ.Tupaia and James are both strong on..

HistoryLanguageGraphicsMaths applied to navigation (Tupaia with sun, stars, wind, swells, clouds, birds and stochastic logic) (James with chronometer, sextant, logs and deterministic logic)Stats applied to demography (Tupaia estimated the size of military groups, James extrapolated to estimate the population of Tahiti)

There are two heritages.

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Equity, Ethnicity and InterventionA country has 2 Ethnicities,

A (the majority) and B.

The results of a survey are shown.

Is there equity in income?

If not, where should interventions be applied??

What subject is this???

(This happens!!)

Income ($1000/year) with Education (Years of Sec+Tert Ed)

for Ethnicities A and B

0

10

20

30

40

50

60

0 5 10 15

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Quakes and SpinsIn the past, earthquakes were seen as

stochastic in space and time (and nasty)

Now, we have:large qnd classy datasetssoftware that can let us look into the data’s structurevisualisation skills

and all these are available to schools.

an Excel interlude….

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Workshop 2: Stats and your Essential Learning AreaPlease team up with people from your ELA or with similar

interests.

1 Think up an “investigation” with a dataset in it.

2 What Curriculum Level does it belong at?

3 What statistical skills does it cal on?

4 How do we get the skills and the links into curriculum documents?

5 Or.. Go back to Equity, Ethnicity and Intervention;slide 26.

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Conclusions: 1/5Into a blossoming future for Maths and Stats EdThere’s a sea of information on statistical…curriculumpedagogyteacher supportresources (including software)assessment.

We need to take a swim into it!It includes:ICOTS conferences (next: Brazil 2006)Online and free SERJ and JSEIASE Roundtable (Jul 2005; Sweden). On CurriculumTeaching StatisticsAmerican Statistician, May 03; Special Section on Stat Ed

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Conclusions: The Good Stuff 2/5Current curriculum has some outstanding strengths:

the focus on Investigationsthe progression through investigation types and variable types.

We can’t lose that.

But we can’t rest on our laurels:Statistics has moved a huge distance since the mid 1980’s.The Links have yet to be created;There are conversations that have only just started.

There’s progress in the draftMaths and Stats Essence Statement

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Conclusions: The New Stats Strand 3/5This time, it won’t be built top-down and in a hurry.

The statistical community must be enabled to take leadership to work on it with all parties: teachers at all levels curriculum experts.

Quality must be designed in;it can’t be patched in at the bottom of the cliff.

This is a great opportunity!

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Conclusion: Research, Resources, PD 4/5We’re impressed by the care, expertise and work that went

into Numeracy.

We’d like an effort modelled on this for Stats:A scan of the sea of recent researchcurriculum analysisresource production, for: stats within maths stats everywhere else; “at large”research into how professional development can be best designedsupport for teachers at every stage.

It’ll need fresh work on how to get Interconnectedness

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Conclusions: For Statistics to blossom… 5/5We need to build capability in teaching (content and pedagogy) teacher education and support (pre and inservice) resource production curriculum design assessment design research in all the aboveWe need careful construction of Links.We need a new engine for leading statistical education!We all need each other!!!

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NZ, with Quakes and 4 Main Centres shown:

A

C

D

2 226 384 226 3843 -101 110 -101 1104 142 339 142 3395 209 467 209 4676 142 339 142 3397 204 468 204 4688 248 444 248 4449 -160 31 -160 31

11 206 498 206 49812 117 350 117 35013 131 384 131 38414 257 462 257 46215 95 261 95 26116 103 297 103 29717 135 385 135 38521 248 375 248 375-800

-400

0

400

800

-800 -400 0 400 800

-800

-400

0

400

800

-800 -300 200 700

A

WW

C

D

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Quakes: Depth vs Distance SouthEast of Wgtn

-800

-400

0

400

800

-800 -300 200 700

statistics in the nz curriculum stocktake

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